Cost allocation in spanning network enterprises with stochastic connection costs

This paper considers the problem of network formation and cost allocation that arises when customers need to be connected to a single service provider through a (communication) network. The cost of a connection consists of both the construction costs and the maintenance costs. Since the latter costs are unknown ex ante connection costs are represented by random variables. It is shown how an ‘optimal’ network is determined and that the core of the corresponding stochastic spanning tree game is non-empty. A two stage Bird allocation is defined and shown to be a core allocation of stochastic spanning tree games.     

The minimal dominant set is a non-empty core-extension

A set of outcomes for a transferable utility game in characteristic function form is dominant if it is, with respect to an outsider-independent dominance relation, accessible and closed. This outsider-independent dominance relation is restrictive in the sense that a deviating coalition cannot determine the payoffs of those coalitions that are not involved in the deviation. Each game generates a unique minimal (for inclusion) dominant set. This minimal dominant set is non-empty and returns the coalition structure core in case this core is non-empty. We provide an algorithm to find the minimal dominant set.     

The core in an oligopoly market with indivisibility

Summary. This paper studies the core in an oligopoly market with indivisibility. It provides necessary and sufficient conditions for core existence in a general m-buyer n-seller market with indivisibility. When costs are dominated by opportunity costs (i.e., a firm's variable costs are sufficiently small), the core condition can be characterized by the primitive market parameters. In a 3-2 market with opportunity cost, the core is non-empty if and only if the larger seller's opportunity cost is either sufficiently large or sufficiently small. Received: June 9, 1999; revised version: October 22, 1999     

On the accessibility of core-extensions

Sengupta and Sengupta (1996) study the accessibility of the core of a TU game and show that the core, if non-empty, can be reached from any non-core allocation via a finite sequence of successive blocks. This paper complements the result by showing that when the core is empty, a number of non-empty core-extensions, including the least core and the weak least core (Maschler et al., 1979), the positive core (Orshan and Sudhölter, 2001) and the extended core (Bejan and Gómez, 2009), are accessible in a strong sense, namely each allocation in each of the foregoing core-extensions can be reached from any allocation through a finite sequence of successive blocks.     

A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game

It is well-known that a transferable utility game has a non-empty core if and only if it is balanced. In the class of non-transferable utility games balancedness or the more general π-balancedness due to Billera (SIAM J. Appl. Math. 18 (1970) 567) is a sufficient, but not a necessary condition for the core to be non-empty. This paper gives a natural extension of the π-balancedness condition that is both necessary and sufficient for non-emptiness of the core.     

Market Games in Large Economies with a Finite Number of Types

We study market games derived from an exchange economy with a continuum of agents, each having one of finitely many possible types. The type of agent determines his initial endowment and utility function. It is shown that, unlike the well-known Shapley–Shubik theorem on market games (Shapley and Shubik in J Econ Theory 1:9–25, 1969), there might be a (fuzzy) game in which each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a game needs also to be homogeneous. We also study investment games – which are fuzzy games obtained from an economy with a finite number of agents cooperating in one or more joint projects. It is argued that the usual definition of the core is inappropriate for such a model. We therefore introduce and analyze the new notion of comprehensive core. This solution concept seems to be more suitable for such a scenario. We finally refer to the notion of feasibility of an allocation in games with a large number of players. Some of the results in this paper appear in a previous draft distributed by the name “Cooperative investment games or Population games”. An anonymous referee of Economic Theory is acknowledged for his/her comments     

The least core, kernel and bargaining sets of large games

Summary. We study the least core, the kernel and bargaining sets of coalitional games with a countable set of players. We show that the least core of a continuous superadditive game with a countable set of players is a non-empty (norm-compact) subset of the space of all countably additive measures. Then we show that in such games the intersection of the prekernel and the least core is non-empty. Finally, we show that the Aumann-Maschler and the Mas-Colell bargaining sets contain the set of all countably additive payoff measures in the prekernel. Received: June 6, 1996; revised version: March 1, 1997     

The minimum cost spanning forest game

We generalize the well-known minimum cost spanning tree game by introducing multiple sources. A forest solution ensues which accounts for competition among the various sources. Using this solution, we show that the core of the induced game is non-empty.     

The core as the set of eventually stable outcomes: A note

As a justification of the core as a set of stable social states, Sengupta and Sengupta [1996. A property of the core. Games Econ. Behav. 12, 266–273] show that for any transferable utility (TU) cooperative game with non-empty core, for every imputation outside the core there is an element in the core that indirectly dominates the imputation in a desirable way. In this note we show that this appealing property of the core no longer holds even for the class of hyperplane games, an immediate generalization of TU games into the environments without side payments.     

A NOTE ON PRODUCT DIFFERENTIATION IN A LINEAR CITY AND WAGE BARGAINING

Economides (Economics Letters, 1986, 21, pp. 67–71) has shown that within a linear city an equilibrium exists in a two‐stage location–price game when the curvature of the transportation cost function is sufficiently high. One important point is that not all of these equilibria are at maximal differentiation. In this paper, we include an additional stage with decentralized wage bargaining. This intensifies price competition resulting in locations that are nearer to the extremes of the city. The magnitude of this effect depends on the bargaining power of the unions. Contrary to the model with exogenously given costs, if unions are sufficient strong all price equilibria in pure strategies are at maximal differentiation. With a low parameter for the curvature of the transportation cost function unions can improve the location decision from a social viewpoint.     

ASYMMETRIC INFORMATION AND EXCHANGE OF INFORMATION ABOUT PRODUCT DIFFERENTIATION

We introduce asymmetric information about consumers’ transportation costs (i.e., the degree of product differentiation) in the model of Hotelling. When transportation costs are high, both firms have lower profits with asymmetric information than with perfect information. Contrarily, if transportation costs are low, both firms may prefer the asymmetric information scenario (the informed firm always prefers the informational advantage, while the uninformed firm may or may not prefer to remain uninformed). Information exchange is ex‐ante advantageous for both firms, but ex‐post damaging if transportation costs turn out to be low. If the information is unverifiable, the informed firm does not represent a reliable source of information, since it always prefers to announce that transportation costs are high and there is no contract that induces truthful revelation.     

A characterization of social choice correspondences that implement the core of simple games

In a coalitional voting game, an alternative is said to be in the core when no majority is willing to replace it with another alternative. A social choice correspondence is a mapping which associates any profile of voters’ preferences with a non-empty subset of the set of alternatives, which is understood as the set of selected outcomes. We characterize the social choice correspondences which always select the core of a simple game for any profile of preferences. This work was completed when B. Tchantcho was Visiting assistant Professor at UTA (University of Texas at Arlington). We acknowledge the support of the Department of Mathematics of UTA. We are most grateful to R. Pongou of Brown University, USA for his help and advice. We sincerely thank N.G Andjiga for his helpful comments and we are indebted to two anonymous referees for their helpful comments.     

A “Super” Folk Theorem for dynastic repeated games

We analyze dynastic repeated games. These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained by sequential equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n  ≥  4 players for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize fully the conditions under which a sequential equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a subgame perfect equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “inter-generational agreement.” A previous version of this paper was circulated as Anderlini et al. (2005). We are grateful to Jeff Ely, Leonardo Felli, Navin Kartik, David Levine, Stephen Morris, Michele Piccione, Andrew Postlewaite, Lones Smith and to seminar audiences at Bocconi, Cambridge, CEPR-Guerzensee, Chicago, Columbia, Edinburgh, Essex, Georgetown, Leicester, LSE, Northwestern, Oxford, Rome (La Sapienza), Rutgers, SAET-Vigo, Stanford, SUNY-Albany, UCL, UC-San Diego, Venice and Yale for helpful feedback.     

Informational size and the incentive compatible coarse core in quasilinear economies

In this paper we show that in quasilinear economies the incentive compatible coarse core is non-empty if agents are informationally small in the sense of McLean and Postlewaite (2002) and the strict core in each state is non-empty.     

An elementary proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley Theorem

Summary This note provides an elementary short proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley (K-K-M-S) Theorem based on Brouwer's fixed point theorem. The usefulness of the K-K-M-S Theorem lies in the fact that it can be applied to prove directly Scarf's (1967) Theorem, i.e. any balanced game has a non-empty core. We also show that the K-K-M-S Theorem and the Gale-Nikaido-Debreu Theorem can be proved by the same arguments.We wish to thank Roko Aliprantis for useful comments.     

A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems

In this paper we present an axiomatic characterization of the weighted Shapley value of the optimistic TU game associated with a minimum cost spanning tree problem. This characterization is based on two monotonicity properties, population monotonicity (if a new agent joint the society nobody is worse off) and the strong cost monotonicity (if the connection cost between any pair of agents increases nobody is better off), and weighted share of extra costs (the extra costs should be divided proportionally to the weights of the agents).      

Lobbying and the power of multinational firms

Can multinational firms exert more power than national firms by influencing politics through lobbying? To answer this question, we analyze the extent of national environmental regulation when policy is determined in a lobbying game between a government and a firm. We compare the resulting equilibrium regulation levels, outputs and welfare in a game with a multinational firm with those in an otherwise identical game with a national firm. For low transportation costs, output and pollution of a national firm are always as least as high as for a multinational; this changes for high transportation costs and intermediate damage parameters. When there is no lobbying, welfare levels are always higher with multinationals than with national firms. However, the existence of lobbying may reverse this ordering.     

A weak bargaining set for contract choice problems

In this paper, we consider the problem of choosing a set of multi-party contracts, where each coalition of agents has a non-empty finite set of feasible contracts to choose from. We call such problems, contract choice problems. The main result in this paper states that every contract choice problem has a non-empty weak bargaining set. The need for such a solution concept which is considerably weaker than the core arises, since it is well-known that even for very simple contract choice problems, the core may be empty. We also show by means of an example that an analog of the bargaining set due to Mas-Colell [Mas-Colell, A., 1989. An equivalence theorem for a bargaining set. Journal of Mathematical Economics 18, 129–139], as well as the natural analog of the bargaining set due to Aumann and Mashler [Aumann, R., Maschler, M., 1964. The bargaining set for cooperative games. In: Dresher, M., Shapley, L., Tucker, A. (Eds.), Advances in Game Theory. Princeton University Press, Princeton, NJ] may be empty for contract choice problems.     

Bilateral versus Multilateral Free Trade Agreements: A Welfare Analysis

Why is a proliferation of bilateral free trade agreements (FTAs) between certain types of countries observed instead of progress in attaining global free trade through a multilateral FTA? This paper answers this question by exploring the enforceability of different types of FTAs through comparing minimum discount factors that are necessary to sustain them in an infinitely repeated game framework. The authors search for the globally welfare maximizing trade agreements that are sustainable under different conditions. The results depict that transportation costs, differences in country sizes and comparative advantages are all obstacles for having a multilateral FTA. Accordingly, international development policies conducted for the removal of such obstacles should be the main goal toward achieving a multilateral FTA, which is shown to be the first‐best solution to the maximization problem of global welfare.     

The circular road revisited: Uniqueness and supermodularity

The model of the circular road has proved to be a popular model of oligopolistic interaction, yet its theoretical properties are not fully explored. In this paper I extend the uniqueness result of price equilibrium in the circular road with equidistant locations from quadratic transportation costs, to a class of convex power transportation costs, i.e. I show uniqueness in oligopoly for a class of utility functions of the consumers. I show that the associated game is supermodular and dominance solvable. The paper also discusses possible extensions and limitations of the model.